(OEIS A077142). Hadamard used the Weierstrass product theorem to derive this result. The plot above shows the convergence of
the formula along the real axis using the first 100 (red), 500 (yellow), 1000 (green),
and 2000 (blue) Riemann zeta function zeros.
The product can also be stated in the alternate form
Havil, J. Gamma: Exploring Euler's Constant. Princeton, NJ: Princeton University Press, 2003.Sloane,
N. J. A. Sequence A077142 in "The
On-Line Encyclopedia of Integer Sequences."Titchmarsh, E. C.
The
Theory of the Riemann Zeta Function, 2nd ed. New York: Clarendon Press, 1987.Voros,
A. "Spectral Functions, Special Functions and the Selberg Zeta Function."
Commun. Math. Phys.110, 439-465, 1987.
as a product over its nontrivial zeros 
,
![zeta(s)=(e^([ln(2pi)-1-gamma/2]s))/(2(s-1)Gamma(1+1/2s))product_(rho)(1-s/rho)e^(s/rho),](/images/equations/HadamardProduct/NumberedEquation1.svg)
is the Euler-Mascheroni constant and
is the Gamma
function (Titchmarsh 1987, Voros 1987). The constant in the exponent is given
by
is the xi-function and
